The Maximum Number of Appearances of a Word in a Grid
Combinatorics
2022-07-26 v1
Abstract
How can you fill a grid with the letters A and M so that the word ``AMM'' appears as many times as possible in the grid? More generally, given a word of length , how can you fill an grid so that appears as many times as possible? We solve this problem exactly for several families of words, and we asymptotically solve this problem in higher-dimensional grids.
Keywords
Cite
@article{arxiv.2207.11273,
title = {The Maximum Number of Appearances of a Word in a Grid},
author = {Gregory Patchell and Sam Spiro},
journal= {arXiv preprint arXiv:2207.11273},
year = {2022}
}
Comments
21 pages, American Mathematically Monthly